# tensor

## Definitions

• WordNet 3.6
• n tensor any of several muscles that cause an attached structure to become tense or firm
• n tensor a generalization of the concept of a vector
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Webster's Revised Unabridged Dictionary
• Tensor (Anat) A muscle that stretches a part, or renders it tense.
• Tensor (Geom) The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
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Century Dictionary and Cyclopedia
• n tensor In anatomy, one of several muscles which tighten a part, or make it tense, or put it upon the stretch: differing from an extensor in not changing the relative position or direction of the axis of the part: opposed to laxator.
• n tensor In mathematics, the modulus of a quaternion; the ratio in which it stretches the length of a vector. If the quaternion is put into the form xi + yj + zk + w, the tensor is √ (x + y +z + w). If the quaternion is expressed as a matrix, the tensor is the square root of the determinant of the matrix. Abbreviated T.
• tensor In anatomy, noting certain muscles whose function is to render fasciæ or other structures tense.
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Chambers's Twentieth Century Dictionary
• n Tensor a muscle that tightens a part
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## Etymology

Webster's Revised Unabridged Dictionary
NL. See Tension
Chambers's Twentieth Century Dictionary
L. tensus, pa.p. of tendĕre, to stretch.

## Usage

### In literature:

The chief physiological antagonistics of the glutei are the quadriceps femoris and tensor fascia lata.
"Lameness of the Horse" by John Victor Lacroix
This fact is expressed by saying that the ten J's form a 'tensor.
"The Concept of Nature" by Alfred North Whitehead
Tensor: a muscle which stretches a membrane.
"Explanation of Terms Used in Entomology" by John. B. Smith
C. External pterygoid process lying on the levator and tensor palati muscles.
"Surgical Anatomy" by Joseph Maclise
He has succeeded in proving experimentally the concept of tensors.
"The Einstein See-Saw" by Miles John Breuer
Some of the operations of tensor calculus have analogs in algebra; many do not.
"Fifty Per Cent Prophet" by Gordon Randall Garrett
He was in authority over Tensor, and therefore far inferior in native gifts.
"Fair and Warmer" by E. G. von Wald
It is covered in front by the tensor of the fascia lata, and contributes with the vastus externus to form the upper prominence of the knee.
"Artistic Anatomy of Animals" by Édouard Cuyer
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### In news:

MineNet is Tensor Technologies' self-described World Wide Web gateway for the mining industry.
We introduce a novel generative Bayesian probabilistic model for unsupervised matrix and tensor factorization.
This paper develops a statistical inference approach, Bayesian Tensor Inference, for style transformation between photo images and sketch images of human faces.
Diffusion tensor imaging (DTI) is a rapidly growing area of interest in radiology research.
Applications of diffusion tensor imaging and fiber tractography.
Diffusion tensor imaging (DTI) and fiber tractography may prove useful in clinical neuroradiology practice in several categories of disease.
Researchers conducted cognitive tests and used advanced brain scans called diffusion tensor imaging (DTI) to compare the brains of 15 children who experienced a concussion within the past 21 days with the brains of 15 unaffected children.
This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry )--the study of a smooth manifold furnished with a metric tensor of arbitrary signature.
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### In science:

The Ricci tensor Rik , the Ricci scalar R and the energy–momentum tensor Tik are deﬁned by .
The Kerr-Schild ansatz for the Nariai spacetime and the generating conjecture
On M × N , we consider an arbitrary tensor of type (1, 2), denoted by P , with αi (a, x) and P j all components null except P β αi (a, x), where α, β = 1, m, i, j = 1, n, which will be called tensor of connection.
Harmonic Maps between Generalized Lagrange Spaces
For every tensor category C there is a braided tensor category Z (C ), the ‘center’ of C .
From Subfactors to Categories and Topology II. The quantum double of tensor categories and subfactors
HomB⊂A (B , B ) is braided equivalent to the sub-tensor category of Z1 (C ) generated by those simple objects (X, eX ) ∈ Z1 (C ) for which X contains the tensor unit 1 of C .
From Subfactors to Categories and Topology II. The quantum double of tensor categories and subfactors
The unadorned tensor product ⊗ means tensor product over k .
Invariant Cyclic Homology
Extended tensor ﬁeld X of type (r, s) in v-representation is a tensor-valued function with argument q = (p, v) in tangent bundle T M and with value X(q) in tensor space T r s (p, M ), where p = π(q).
On the concept of normal shift in non-metric geometry
What are the corresponding equations for antisymmetric tensor ﬁeld? Proca? Maxwell? Recently we have shown [14,16] that one can obtain four different equations for antisymmetric tensor ﬁelds from the Weinberg 2(2J + 1) component formalism.
Generalizations of the Dirac Equation and the Modified Bargmann-Wigner Formalism
This complies with the fact that the canonical AdS stress-energy tensor is a density in AdS, while the stressenergy tensor for the generalized free ﬁeld on the boundary is a density in Minkowski space.
Generalized free fields and the AdS-CFT correspondence
The purpose of this section is to ﬁnd a stress-energy tensor Θµν (x) for the generalized free ﬁeld (2.1) which has the properties of a local and covariant conserved tensor density for the generators of the Poincar´e group.
Generalized free fields and the AdS-CFT correspondence
To do this, it suﬃces to calculate the mean value the tensor product JN ⊗ JN , because the determinant of 2×2-matrix is a linear function of the elements of its tensor square.
Random groups in the optical waveguides theory
Further, since JN is an integral over the parameter β of matrices JN (β ), the mentioned tensor product is the integral over the pair (β1 , β2 ) of the tensor product JN (β1 ) ⊗ JN (β2 ).
Random groups in the optical waveguides theory
F is the forcing and the stress tensor T is determined by the polymer conformation tensor R according to τp (cid:20) f (r , t) R(r , t) − 1(cid:21) .
A simple model for drag reduction
Lepowsky, Tensor products of modules for a vertex operator algebra and vertex tensor categories, in: Lie Theory and Geometry, ed. R.
Module categories of simple current extensions of vertex operator algebras
The algebra in the tensor product space is connected with Hopf algebras such that the coproduct map ∆ of Hopf algebras is a homomorphism to the tensor product space ∆ : A → A ⊗ A.
Generalized exclusion and Hopf algebras
In other words, the connection is written as the sum of the Christoffel symbol and an extra tensor deﬁned by the torsion tensor τ α µν .
Geometrical description of spin-2 fields
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